As protection against ground faults on double lines, according to the state of the art distance relays are usually used, which are normally based on impedance measurement. Within the current technical field these are so well-known that no further description of them will be made. Different embodiments are disclosed, for example, in U.S. Pat. No. 4,636,909 (Brandt).
As mentioned by way of introduction, the use of impedance based protection devices in connection with double lines entails certain problems of distinguishing faults, for example when a phase fault in different phases occurs on the lines at short time intervals. This has proved to be particularly difficult on double line systems which comprise series capacitors. In the case of a fault according to the above, in this situation normally all the phases of a conventional distance relay trip, which is due to the fact that they are not capable of distinguishing the situation from the case where a multi-phase fault has occurred in one of the double lines. Thus, all three phases are disconnected, even when in reality it would have been possible to break only the faulty phase.
The impedance plane analysis can be performed both analogically and with the aid of computerized programs. In an article by Phadke and Jihuang published in IEEE Trans. on PAS, Vol. PAS-104, No. 2, February 1985, pp. 445-452, entitled "A Computer Based Integrated Distance Relay for Parallel Transmission Lines", a method is described which is based on impedance plane analysis of the status of the line seen from one end. A measuring point is placed at one end of each line and the results are coordinated. However, this may be a dangerous method since it may be difficult to analyze such cases where the fault occurs in the vicinity of the other end of the line. A method of overcoming this deficiency is provided by the technique described in EP 0 015 259 entitled "A method and a device for detection of the position of a fault in an electric connection". According to this method, a relay unit is used at each end and each line of the protected line zone. However, also in this case there is still a need to study impedances to determine in what phase(s) and what line all the faults occur.
The technical basis for protection using selective phase selection in connection with double lines according to the invention is based on the technique which is described in detail in U.S. patent applications Ser. Nos. 241,370 and 262,742, respectively. A brief resume of these applications will be given here.
Measured signals for phase currents and phase voltages obtained from the power network are transformed, after filtering and digitization, into an analytical model in the form of a harmonic truncated Fourier series (M=a.sub.1 sin .omega..sub.0 t+a.sub.2 cos .omega..sub.0 t). The Fourier coefficients are determined in a parameter estimator operating with an estimation method according to the least squares method. With the aid of the model an exact calculation can be made of the fundamental frequency of the model in a frequency estimator, the output signal of which is returned to the parameter estimator. U.S. application Ser. No. 241,370 shows, for example, that the angular frequency .omega. for the model can be calculated with the aid of three consecutive sample values y.sub.1, y.sub.2, y.sub.3 of the processed signal as ##EQU1## where h is the distance in time between the sample values.
The current parameter estimation method will be clear from the following.
The measured signals in question can, in general, be modelled by ##EQU2## which can be transformed into EQU y(t)=.theta..sup.T .phi.(t) (2)
where EQU .theta..sup.T =(a.sub.0, -c.sub.0 b.sub.0, c.sub.1 cos d.sub.1, c.sub.1 sin d.sub.1, . . . c.sub.N cos d.sub.N, c.sub.N sin d.sub.N) (3)
is a parameter vector and EQU .phi.(t)=(1, t, sin .omega..sub.0 t, cos .omega..sub.0 t, . . . sin N.omega..sub.0 t, cos N.omega..sub.0 t) (4)
is a regression vector.
Estimation of the parameters according to the least squares method entails that the value of a "loss function" V.sub.N is minimized. V.sub.N can be written as ##EQU3## where .lambda. is a forgetting factor and where .epsilon.(t) is an estimation error function (a residual) as defined by (11).
The minimization gives the following equation to compute an estimation to .theta.(t), .theta. ##EQU4##
The actual estimation is performed recursively with the aid of the following algorithm EQU R(t)=.lambda..multidot.R(t-1)+.phi.(t).phi..sup.T (t) (7) EQU R(O)=.delta..multidot.I (8) EQU R(t)L(t)=.phi.(t) (9) EQU y(t)=.theta..sup.T (t-1).phi.(t) (10) EQU .epsilon.(t)=y(t)-y(t) (11) EQU .theta.(t)=.theta.(t-1)+L(t).epsilon.(t) (12).
Here, R(t) is the covariance matrix of the regression vector and P(t), according to the following, is the inverse thereof. Otherwise, the following recurrence formulae will be used: EQU r(t)=P(t-1).phi.(t) (13) EQU d(t)=.lambda.+.phi..sup.T (t)r(t) (14) EQU L(t)=r(t)/d(t) (15) EQU P(t)=(P(t-1)-r(t)L.sup.T (t))/.lambda. (16) EQU P(O)=(1/.delta.).multidot.I (17) EQU .theta.(O)=.theta..sub.0 ( 18).
Otherwise, the same criteria as are used in the above-mentioned Swedish applications are used in this protective concept as well as regards phase selection and determination of direction to a fault and as regards the possibilities of distinguishing a fault situation from a connection or disconnection of a phase and/or a line.
These criteria can be described as follows. A test whether an abrupt event has occurred is performed as a transient analysis of suitable loss functions according to (5) by comparing the values of the functions against set threshold values. If the limit values have been exceeded, a steady state analysis is performed in order to find out whether the event is due to a fault or to a connection/disconnection of a phase and/or a line. This can be done by a study of the Fourier components before and after the event. If the result of this analysis shows that a fault has occurred, the faulty phase can be determined by the study of the loss function of th phase voltages or by a study of the amplitude of the harmonics.
Knowledge of the direction to a fault can be obtained by finding out the current direction of the two end points, which can be done with the aid of a study of the polarity of the current residuals after the determination of a fault. This presupposes that measuring stations are provided on both sides of the protected line and the communication facilities are provided between the two ends of the line. To determine whether the fault occurs in the protected line, it is sufficient to study two situations, namely, whether the currents at both end points are directed away from the line or towards the line. In both of these cases the fault is located on the protected line if the signs on the residuals are the same.